Hyers–Ulam and Hyers–Ulam–Rassias Stability for Linear Fractional Systems with Riemann–Liouville Derivatives and Distributed Delays

The aim of the present paper is to study asymptotic properties solutions linear fractional system with Riemann–Liouville-type derivatives and distributed delays. We prove under natural assumptions (similar those used in case when are first (integer) order) existence uniqueness initial problem for these systems discontinuous functions. As a consequence, we also unique fundamental matrix homogeneous system, which allows us establish an integral representation corresponding inhomogeneous system. Then, introduce studied concept Hyers–Ulam time stability Hyers–Ulam–Rassias stability. application obtained results, propose new approach (instead standard fixed point approach) based on sufficient conditions, guarantee Hyers–Ulam-type time. Finally, it proved that leads Lyapunov investigated systems.